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An Improved Method for Nonlinear Variable-Order Lévy–Feller Advection–Dispersion Equation

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Abstract

In this paper, numerical investigations of the variable-order fractional Lévy–Feller advection–dispersion equation with a nonlinear source term are presented. A family of time stepping schemes is proposed to solve this equation with space performed by the spectral Chebyshev–Legendre collocation method. The proposed methods reduce these types of partial differential equations to a system of nonlinear algebraic equations which is far easier to be solved. The numerical results of these methods have been compared with the results of other methods to show the good computationally performance, accuracy and efficiency of the presented schemes.

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Acknowledgements

The authors are indebted to the referees for constructive observations and remarks which have improved the paper. These have been fully taken in consideration.

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  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    N. H. Sweilam & M. M. Abou Hasan

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  1. N. H. Sweilam
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  2. M. M. Abou Hasan
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Correspondence to N. H. Sweilam.

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Communicated by Ahmad Izani Md. Ismail.

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Sweilam, N.H., Hasan, M.M.A. An Improved Method for Nonlinear Variable-Order Lévy–Feller Advection–Dispersion Equation. Bull. Malays. Math. Sci. Soc. 42, 3021–3046 (2019). https://doi.org/10.1007/s40840-018-0644-7

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  • DOI: https://doi.org/10.1007/s40840-018-0644-7

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